Presentations and Tietze transformations of C*-algebras

TL;DR

This paper introduces a new presentation theory for C*-algebras, including Tietze transformations, establishing a transformation theorem similar to classical results in group theory.

Contribution

It develops a novel framework for presenting C*-algebras and introduces Tietze transformations, bridging algebraic presentation theory with operator algebras.

Findings

Defined Tietze transformations for C*-algebra presentations

Proved a transformation theorem analogous to Tietze's result in group theory

Established a new perspective on algebraic presentations of C*-algebras

Abstract

In this work, I develop a new view of presentation theory for C*-algebras, both unital and non-unital, heavily grounded in classical notions from algebra. In particular, I introduce Tietze transformations for these presentations, which lead to a transformation theorem analogous to Tietze's 1908 result in group theory.